In CT systems, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system, termed the "imaging plane". The x-ray beam passes through the object being imaged, such as a patient, and impinges upon a linear array of radiation detectors. The intensity of the transmitted radiation is dependent upon the attenuation of the x-ray beam by the object. Each detector of the linear array produces a separate electrical signal that is a measurement of the beam attenuation. The attenuation measurements from all the detectors are acquired separately to produce a transmission profile.
The x-ray source and the linear detector array in a CT system are rotated with a gantry within the imaging plane and around the object so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements from the detector array at one gantry angle is referred to as a "view". A "scan" of the object comprises a set of views made at different gantry angles during one revolution of the x-ray source and detector. In an axial scan, data is processed to construct an image that corresponds to a two dimensional slice taken through the object. One method for reconstructing an image from a set of data is referred to in the art as the filtered back projection technique. This process converts the attenuation measurements from a scan into integers called "CT numbers" or "Hounsfield units", which are used to control the brightness of a corresponding pixel on a cathode ray tube display.
Computed tomograph scans have been acquired with a stop-and-shoot technique. With the stop and shoot method, a complete set of projections is acquired before the patient is translated to a next location. To ensure image quality, a non-zero inter-scan delay (ISD) is introduced between scans. The ISD is typically long enough to ensure that the gantry rotates at a constant speed while obtaining projection data and that the patient moves to the next location and stops before a next scan is initiated. At least with respect to patient throughput, this mode of scanning is not efficient.
CT scans also may be acquired using a continuous data acquisition technique. In this mode, both the gantry and the patient move at a constant speed. The data acquisition is continuous throughout the entire process. This scanning mode is known as a helical or spiral scan.
Although helical scanning has many advantages (e.g., arbitrary location image reconstruction and improved patient throughput), there also are some disadvantages. For example, a basic assumption of tomographic reconstruction theory assumes that each projection in a data set represents line integrals of the same object. That is, the distribution of the attenuation map remains unchanged in the reconstruction plane. When a non-homogeneous object is scanned in the helical mode, the object is constantly translated during the data acquisition. Due to the heterogeneity of the object, the attenuation distribution inside the scanning plane changes constantly. These continuous changes clearly violate the basic assumption of the tomographic reconstruction theory. If the projection data is not properly corrected for the object translation, undesirable image artifacts will result.
Various correction algorithms to address the heterogeneity issue are known. For example, a helical extrapolative (HE) algorithm is described in U.S. Pat. No. 5,233,518 which is assigned to the present assignee. The HE algorithm is based upon the fact that each set of helical projections can be divided into two sets of half scans. By performing interpolation and extrapolation, a more consistent set of projections at a predefined slice plane can be obtained. Due to the nature of the fan beam geometry, the weighting function derived from the algorithm is not continuous along a line in Radon space. To avoid any artifacts caused by this discontinuity, a feathering algorithm which ensures a smoother transition between the two regions is employed. The nature of the extrapolation also produces weights that are negative or greater than one.
It would be desirable to provide an interpolative algorithm which is more stable than its extrapolative counterpart. In addition it would be desirable to eliminate a need for a feathering algorithm to ensure an artifact free reconstruction and to improve the noise characteristics of such reconstruction.